A nonlinear model of thermoelastic beams with voids, with applications

Abstract

We generalize the traditional Hamilton principle and give a complete nonlinear mathematical model of thermoelastic beams with voids based on this generalization, including the influences of the axial force, neutral layer inertia and rotation inertia. The differential quadrature method is used to discrete the nonlinear system on the spatial domain, and the Newton-Raphson method and Runge-Kutta method are adopted to solve the static and dynamical behaviors of the beam, respectively. The influences of the parameters on the nonlinear mechanical behavior of beam are studied in detail. The results show that the presence of voids enlarges beam deflection. And also one can see that the DQM has advantages of fewer workload, higher precision, better convergence, and so on.

Response of Thermoelastic Beam due to Thermal Source in Modified Couple Stress Theory

“…Sun et al [11] used the Laplace transform technique to study the vibration phenomena due to pulsed laser heating of a microbeam under different boundary conditions. Thermoelastic beams with voids were studied by Li and Cheng [12]. Sharma [13] derived governing equations of flexural vibrations in a transversely isotropic, thermoelastic beam in a closed form based on the Euler-Bernoulli theory to study thermoelastic damping (TED) and frequency shift (FS) of vibrations in clamped and simply supported beam structures.…”